SCIENCE OF AERONAUTICSAND

ENGINEERING EDUCATION TECHNICS

PI VALUE FROM RIGVEDA

CH. PURUSHOTHAMAERONAUTICAL ENGG.

PI VALUE FROM RIGVEDAMen of older generation used to say that all knowledge is there in the Vedas. Anyone who hears such words will have the first reaction that it is an over confident statement. We should remember here that any sloka in the ancient Hindu manuscripts has more than one meaning.

Katapayadi sankhya is a simplification of Aryabhata ‘s Sanskrit numerals , due probably to Haridatta from Kerala. InMalayalam it is also known as ‘Paralperu’ For eg: represents 31415926536 which is _*1000000000000000

The oldest available evidence of the use of Kaṭapayādi ( कटपयादि�) system is from Grahacāraṇibandhana by Haridatta in 683 CE. It has been used in Laghu·bhāskarīya·vivaraṇa written by Śaṅkara·nārāyaṇa   in 869 CE.

A Sloka in the 10th book of Rig Veda appears to be written for praising Lord IndraThe technical translation of that Sloka gives the value of pi up to 28 digits accurately. It is not until the invention of the computers that the western mathematicians could get this value up to 16 digits accurately. Here is a test for those who think that a computer can do any calculation. Use the fastest computer available to you and write a program to calculate the value of pi up to 28 digits accurately. You will know how difficult it is.

Vedic Numerical CodeIn Sanskrit, the following Vedic Numerical code was used in many slokas.

Means...

कादि� नव Kaadi nava Kaadi Nava Starting from ka, the sequence of 9 letters represent 1,2,..9टादि� नव Taadi nava Taadi Nava starting from ta, the sequence of 9 letters represent 1,2,..9

पादि� पञ्चक Paadi panchaka Paadi panchaka (1-5), starting from paयद्यश्टक Yadyashtaka Yadyashtaka (1-8) starting from yaक्ष शुन्यम् Kshah sunyam ksha represents 0

In detailNa(न), nya(ञ), i.e., vowels represent Zero.

The nine integers are represented by consonant group beginning with ka, ta, pa,ya. In a conjunct consonant, the last of the consonants alone will count.

A consonant without vowel is to be ignored.

KaTaPaYa di for Melakarta Ragam Name & numbers1 2 3 4 5 6 7 8 9 0

క क Ka ఖ ख Kh

a గ ग Ga ఘ घ Gh

a ఙ ङ Gna చ च Ch

a ఛ छ Cha జ ज Ja ఝ झ Jha ఞ ञ nya

ట ट Ta ఠ ठ Th

a డ ड Da ఢ ढ Dh

a ణ ण ~na త त Ta థ थ Tha ద � Da ధ ध Dha న न Na

ప प Pa ఫ फ Ph

a బ ब Ba భ भ Bha మ म Ma

య य Ya ర र Ra ల ल La వ व Va శ श Sa ష ष Sh

a స स Sa హ ह Ha

క్ష क््ष

kshah

గోపీభాగ్యమధువ్రా) త-శృంగిశోదధిసంధిగ | ఖలజీవితఖాతావ గలహాలారసంధర ||

गोपीभाग्य मधुव्रातः श्रुंगशो�धिध संधिधगः |खलजीविवतखाताव गलहाला रसंधरः ||gopeebhaagya maDhuvraathaH shruMgashodhaDhi saMDhigaHkhalajeevithakhaathaava galahaalaa rasaMDharaH

3.1415926535897932384626433832792...

The above sloka has actually 3 meanings1. In favor of Lord Shiva2. In favor of Lord Krishna3. The value of PI upto 32 decimals.

Śaṅkara·varman's Sad·ratna·mālā uses the Kaṭapayādi system. A famous verse found in Sad·ratna·mālā isभद्राम्बुद्धि7सिस7जन्मगणिणतश्र7ा स्म य� ्भूपगी:

Transliterationbhadrāṃbuddhisiddhajanmagaṇitaśraddhā sma yad bhūpagīḥ

Splitting the consonants gives,

भ bha

द�्

d

रा rā

म� ṃ

बु ba

द�्

d

धि dh

सि् sa

द�्

d

dha

ज ja

न�्

n

म ma

ग ga

णि् ṇa

त ta

श�्

ṣ

र ra

द�्

d

ा dha

स�्

s

म ma

य ya

द�्

d

भू bha

प pa

गि् gi

4 - 2 - 3 - 9 7 - 9 8 - 5 3 5 6 - 2 - 9 - 5 1 - 4 1 3

Reversing the digits to modern day usage of descending order of decimal places, we get 314159265358979324 which is the value of pi (π) to 17 decimal places, except the last digit might be rounded off to 4.

Series of PIThere is also a sloka for expanding the series of PI. It's given below.व्यासे वारिरधिधविनहते रूपहृते व्यससागराणिभहते ।विAशरादि�विवषमसंख्याभकं्त ॠणं स्वं पृथक्क्रमात् कुयाHत् ॥

vyAse vaariDhinihathe rUpahtRthevyasasAgarAbhihathethrisharAdhiviShamasMkhyAbhakthM TRNM svM ptRThakkramAth kuryaath

Meaning :When the circumference/perimeter of the circle is given in terms of a series (containing d=diameter) then the diameter term is divided by the odd numbers (like 1, 2, 3...) and alternately added/subtracted fromthe rest (of the summation of series)

i.e:Circumference = 4d/1 - 4d/3 4d/5 – 4d/7 ...which is basically the same series as PI/4 = SUMOF [(-1 i 1)/(2i-1)] /* over i from 1 to infinity */

There were many inventions in the field of science and technology in ancient India. Since many persons of the present generation does not know them, they will be described briefly to enable the readers to have the basic understanding about them.

Reference:

1) http://sanskritum.blogspot.in/2015/02/katapayadi-sankhya-sanskrit-and-pie.html

2) https://en.wikipedia.org/wiki/Katapayadi_system

3) https://www.facebook.com/BHARAT.untoldstory/posts/610567172308226

4) http://bvsubbaiah.tripod.com/blog/index.blog?entry_id=1400661